## An Introduction to Analytical Plane Geometry |

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asymptotes ax˛ axes axis becomes called centre CHAPTER chord circle co-ordinates coincide common condition cone conic conic section conjugate constant corresponding curve denote determining diameter direction directrix distance double draw drawn eccentricity ellipse equal Euclid EXAMPLES expression figure Find the equation focus four geometry given point giving Hence hyperbola imaginary inclined infinite infinity intersection length lies line joining locus meet moves negative normal opposite sides origin parabola parallel passes perpendicular plane point x'y polar pole positive produced projection Prove radius ratio rectangular referred represents respect right angles Similarly sin˛ squares straight line Suppose tangent theorem touch triangle values Y₁ zero

### Popular passages

Page 105 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.

Page 88 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.

Page 42 - A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8.

Page 99 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.

Page 33 - Divide by the square root of the sum of the squares of the coefficients of x and y.

Page 232 - Given four points on a conic, the locus of the pole of a given line is a conic passing through the four points (Chap.

Page 102 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.

Page 7 - The area of a triangle is equal to half the product of two sides and the sine of the included angle.

Page 182 - If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the

Page 101 - The curve y2 = kqx passes through the origin and the line x = 0 is the tangent at the origin. (Art. 100.) For every positive value of x there are two values of y, equal in magnitude and of opposite sign: thus the curve is symmetrical with respect to the axis of x. Also if x be negative, y is impossible. Thus the curve lies wholly on the Ox side of the axis of y. If x be infinitely great, so is y. Thus the curve is of infinite size. 106. To find the equation to the tangent at the point x'y'.